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Simplifying 0 = -1d2 + 10d + 5 Reorder the terms: 0 = 5 + 10d + -1d2 Solving 0 = 5 + 10d + -1d2 Solving for variable 'd'. Combine like terms: 0 + -5 = -5 -5 + -10d + d2 = 5 + 10d + -1d2 + -5 + -10d + d2 Reorder the terms: -5 + -10d + d2 = 5 + -5 + 10d + -10d + -1d2 + d2 Combine like terms: 5 + -5 = 0 -5 + -10d + d2 = 0 + 10d + -10d + -1d2 + d2 -5 + -10d + d2 = 10d + -10d + -1d2 + d2 Combine like terms: 10d + -10d = 0 -5 + -10d + d2 = 0 + -1d2 + d2 -5 + -10d + d2 = -1d2 + d2 Combine like terms: -1d2 + d2 = 0 -5 + -10d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -10d + 5 + d2 = 0 + 5 Reorder the terms: -5 + 5 + -10d + d2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -10d + d2 = 0 + 5 -10d + d2 = 0 + 5 Combine like terms: 0 + 5 = 5 -10d + d2 = 5 The d term is -10d. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10d + 25 + d2 = 5 + 25 Reorder the terms: 25 + -10d + d2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + -10d + d2 = 30 Factor a perfect square on the left side: (d + -5)(d + -5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (d + -5) equal to 5.477225575 and -5.477225575.Subproblem 1
d + -5 = 5.477225575 Simplifying d + -5 = 5.477225575 Reorder the terms: -5 + d = 5.477225575 Solving -5 + d = 5.477225575 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + d = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + d = 5.477225575 + 5 d = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 d = 10.477225575 Simplifying d = 10.477225575Subproblem 2
d + -5 = -5.477225575 Simplifying d + -5 = -5.477225575 Reorder the terms: -5 + d = -5.477225575 Solving -5 + d = -5.477225575 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + d = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + d = -5.477225575 + 5 d = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 d = -0.477225575 Simplifying d = -0.477225575Solution
The solution to the problem is based on the solutions from the subproblems. d = {10.477225575, -0.477225575}
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